Insulate the basement ceiling with fiberglass bats. While fiberglass insulation is not commonly used between indoor living spaces, the insulation helps to dampen noise. Place the insulation bats between each ceiling joist.
Attach mass loaded vinyl (MLV), a heavy vinyl sheeting, to the underside of the ceiling joists. Cut the sheeting to size with a utility knife and staple it to the underside of the ceiling joists.
Carpet the floor above the basement to dampen noise of people walking on a hard surface, such as wood floors. Adding MLV under hard-floor surfaces also improves the sound isolation between the basement and main floor.
Add acoustic tile to the ceiling of the basement. A suspended ceiling provides further sound isolation because the framework of the suspended ceiling hangs by wires from the ceiling joists. There is no direct solid connection between the ceiling and the floor joists of the main floor, stopping vibration from moving between levels.